Chemical Bonding B.Sc. 1st Year

Chemical Bonding

Orbital Overlap Concept

When two atoms approach each other, their atomic orbitals undergo partial interpenetration (overlap). This partial interpenetration of atomic orbitals is called overlapping of atomic orbitals. The electrons belonging to these orbitals are said to be shared and this results in the formation of a covalent bond. The main ideas of overlapping of orbital concept for the covalent bond formation are-
a. Covalent bonds are formed by the overlapping of half filled atomic orbitals present in the valence shell of the atoms taking part in bonding.

b. The orbitals undergoing overlapping must have electrons with opposite spins.
c. Overlapping of atomic orbitals results in decrease of energy and formation of covalent bond.
d. The strength of a covalent bond depends upon the extent of overlapping. The greater the overlapping, the stronger is the bond formed.
The above treatment of formation of covalent bond involving the overlap of half-filled atomic orbitals is called valence bond theory.

Types of Overlapping and Nature of Covalent Bonds

The covalent bond may be classified into two types depending upon the types of overlapping-
A. Sigma(σ) bond, and
B. Pi(π) bond

Sigma(σ) bond

This type of covalent bond is formed by the end to end (hand-on or face to face) overlap of bonding orbitals along the internuclear axis. This can be formed by any one of the following types of combinations of atomic orbitals.

a. s-s overlapping
b. s-s overlapping
c. s-s overlapping

s-s overlapping

s-s overlapping occurs between two half filled s-orbitals along the internuclear axis as shown below-

s-p overlapping

s-p overlapping occurs between half filled s-orbitals of one atom and half filled p-orbitals of another atom.

p-p overlapping

p-p overlapping takes place between half filled p-orbitals of the two approaching atoms.

Pi(π) bond

In the π bond formation, the atomic orbitals overlap in such a way that their axes remain parallel to each other and perpendicular to the internuclear axis (i.e. sidewise overlapping). The orbitals formed due to side wise overlapping consists of two saucer type charged clouds above and below the plane of the participating atoms.

Strength of Sigma and pi Bonds

Strength of a bond depends upon the extent of overlapping. In case of σ bond, the overlapping of orbitals takes place to a larger extent. Hence, it is stronger as compared to the π bond where the extent of overlapping occurs to a smaller extent. Further, it is important to note that π bond between two atoms is formed in addition to a sigma bond. It is always present in the molecules containing multiple bond (double ortriple bonds). Generally σ bond formed first but in case of B₂ and C₂, π bond formed first then σ bond.

Valence Bond Theory (VBT)

This theory was proposed by Heitler and London to explain the formation of covalent bond quantitatively using quantum mechanics. Later on, Linus Pauling improved this theory by introducing the concept of hybridization.
The main postulates of this theory are as follows-
1. It deals with the electronic configuration of the elements.
2. The valency of an element is the number of unpaired electrons present in valence shell of ita atom.
3. The paired electrons of the valence shell does not take part in the bond formation.
4. A covalent bond is formed by the overlapping of two half filled valence atomic orbitals of two different atoms.

5. The electrons in the overlapping orbitals get paired and confined between the nuclei of two atoms.
6. The electron density between two bonded atoms increases due to overlapping. This confers stability to the molecule.
7. Greater the extent of overlapping, stronger is the bond formed.
8. The direction of the covalent bond is along the region of overlapping of the atomic orbitals i.e., covalent bond is directional.
9. There are two types of covalent bonds (sigma and pi) formed based on the pattern of overlapping.

Limitations of Valence Bond Theory

Followings are the limitations of this theory-

1. It does not explain the paramagnatism of oxygen and some other molecules.
2. It does not explain the coordinate bond formation.
3. It fails to explain the bond formation in B₂H₆, H₂⁺, He₂⁺ etc.
4. It totally fails to explain color, kinetics, thermodynamics and structural properties of compounds.

Hybridization

The process of mixing of two or more different atomic orbitals having almost same energy to form equal number of equivalent orbitals called hybrid orbitals and the phenomenon is called hybridization.
hybrid orbitals are different from atomic orbitals and they are directional so they have definite geometrical shape.
Hybridization is hypothetical so it is not possible for every molecules and is of different types but here only six types are given below-
sp Hybridisation

Mixing of one 's' with one 'p' orbitals of almost equal energy to give two identical and degenerate 'sp' hybrid orbitals. These two hybrid orbitals arranged linearly in 3D space. The bond angle is 180^o and they possess 50% 's' and 50% 'p' character.

sp² Hybridisation
Mixing of one 's' with two 'p' orbitals of almost equal energy to give three identical and degenerate sp² hybrid orbitals. These three hybrid orbitals arranged in 3D space as triangular planar. The bond angle is 120^o and they possess 33.3% 's' and 66.6% 'p' character.

sp³ Hybridisation
Mixing of one 's' with three 'p' orbitals of almost equal energy to give four identical and degenerate sp³ hybrid orbitals. These four hybrid orbitals arranged tetrahedrally in 3D space. The bond angle is 109.5^o and they possess 25% 's' and 75% 'p' character.

sp³d Hybridisation
Mixing of one 's' with three 'p' and one d orbitals of almost equal energy to give five identical and degenerate sp³d hybrid orbitals. These five hybrid orbitals arranged in 3D space as triangular bipyramidal. The bond angle are 120^o and 90^o and they possess 20% 's' and 60% 'p' and 20% d character.


sp³d² Hybridisation
Mixing of one 's' with three 'p' and two d orbitals of almost equal energy to give six identical and degenerate sp³d² hybrid orbitals. These six hybrid orbitals arranged in 3D space as octahedral. The bond angle is 90^o and they possess 16.6% 's' and 49.8% 'p' and 33.2% d character.

sp³d³ Hybridisation
Mixing of one 's' with three 'p' and three d orbitals of almost equal energy to give seven identical and degenerate sp³d³ hybrid orbitals. These seven hybrid orbitals arranged in 3D space as pentagonal bipyramidal. The bond angle is 72^o and they possess 14.14% 's' and 42.42% 'p' and 42.42% d character.

Determination of Hybridization

Short Formula
H = 1/2(V + M - C + A)
V= No. of valence electrons of central atom
M- No. Of monovalent atom
C- Total Cation charge
A- Total Anion charge
Example
CH₄
Central atom carbon valence electron (V) = 4

No. of monovalent atom (hydrogen) (M) = 4
In CH₄, there is no chage. So, C and A is zero.
Therefore, H = 1/2(4 + 4) = 4 The value of 4 indicates the hybridization of CH₄ is sp³.

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Other Method
This method involves a number of steps-
1. Calculate the total valence electron (TVE) of the given molecule
2. Calculate the duet/octet electrons
3. Calculate the lone pair electrons in the molecule
4. No. of hybrid orbitals need for bonding (= no. of bonded atoms + no. of L.P.)
5. Calculate the no. of hybrid orbitals

6. Hybridization- According to value of step 5
7. Structure- According to hybridization
8. Shape- if molecules does not have lone pair(s), then structure and shape are same however, if molecules have lone pair(s), then structure and shape are different.
Example
CH₄
TVE = 4 + (1 x 4) = 8
No. of duet electrons = 4 x 2 = 8
No. of Lone Pair = 1/2(8 - 8) = 0
No. of hybrid orbitals need for bonding = 4 + 0 = 4
No. of hybrid orbitals = 4

Hybridization = sp³
Structure = Tetrahedral
Shape = Tetrahedral (as there is no lone pair)

Q. Find out the correct hybridization of P in PH₃ molecule

a. sp³
b. sp²
c. sp²d
d. None of the above

Find out the correct hybridization of Mn in KMnO₄ molecule

a. sp³
b. sd³
c. sp²d
d. None of the above

Valence Sheel Electron Pair Repulsion Theory (VSEPR Theroy)

This theory was proposed by Sidwick and Powell in 1940 and later on modified by Gillespie and Nyholm in 1957.
This theory predict the shape of simple molecules and ions on the basis of repulsion of electron pairs present in the valence shell of their central atom.

Some Important Postulates of this Theory are given below
1. Electrons involved in the bond formation is called bonding electrons or bond pair (B.P.) and the rest electrons are called lone pairs (L.P.).
2. Electron pairs in valence shell repel one-another as electron clouds are negatively charged.
3. These electron pairs occupy the space at maximum distance for minimum repulsion.
4. The most stable geometrical arrangement of 2,3,4,5,6 electron pairs is linear, triangular, tetrahedral, triangular bipyramidal and octahedral respectively.
5. The central atom in a molecule is surrounded by only B.P. the molecule has regular or symmetrical geometry but in case of B.P. and L.P. the molecule does not have regular geometry.
6. A lone pair occupies more space than a bond pair because lone pair attached with only one atom. Hence the order of repulsion is-
L.P - L.P. > L.P - B.P. > B.P - B.P.

Greater the repulsion, smaller the bond angle.
7. Multiple bonds does not affect the gross geometry of the molecules rather the geometry is exclusively decided by B.P. and L.P.
8. A lone pair and double bond repulsion is much greater than a lone electron and double bond repulsion.
9. A lone pair and a single bond repulsion is larger than a lone pair and double bond repulsion.

Geometries of molecules from VSEPR Theory

Polarization And Polarizability

The ability of a cation to polarize the anion is referred to as polarizing power. It is directly proportional to the charge density, which in turn is directly related to the charge on cation, while inversely related to the size of anion.

The polarizing power increases with increase in the size of cation i.e. smaller cations are very effective in the polarization of anion. However, the polarizing power increases with increase in the charge on cation (i.e. smaller cation).
The tendency of an anion to become polarized by the cation is called polarizibility. It indicates the easiness with which an anion undergoes distortion in presence of a cation.
It is directly proportional to the size and the charge on an anion. The larger anions can polarized very easily than the smaller ones.
From the above discussion we can easily say that greater the polarizing power of cation and greater the polarizability of anion, greater is the polarization and hence greater will be the covalent nature.

Polarization is the distortion of the shape of an anion by an adjacently placed cation. Which of the following statements is correct

a. Maximum polarization is brought about by a cation of high charge
b. A large cation is likely to bring about a large degree of polarization
c. Minimum polarization is brought about by a cation of low radius
d. A small anion is likely to undergo a large degree of polarization

Polarisibility of halide ions increases in the order

a. F^-, I^-, Br^-, Cl^-
b. Cl^-, Br^-, I^-, F^-
c. I^-, Br^-, Cl^-, F^-
d. F^-, Cl^-, Br^-, I^-

Polarization power of cation increases when

a. size decrease
b. size increases
c. Anion has greater polarizing power
d. covalent nature increases

Polarising power is directly proportional to

a. size of cation
b. charge on cation
c. electronegativity of cation
d. size of anion

Fajan's Rule

Kazimierz Fajans in 1923, gave some important points to predict whether a chemical bond is expected to be predominantly ionic or covalent.They are given below-
1. Size of Cations
2. Size of Anions
3. Charge on ions (Cations and Anions)
4. 18 electron configuration

1. Size of Cations
Smaller the size of cation, greater the covalent character.
Example: LiCl, NaCl, KCl, RbCl, CsCl
LiCl is most covalent among the given IA chlorides as the size of Li⁺ is smaller than that of other IA cations.
The order of covalent character is-
LiCl > NaCl > KCl > RbCl > CsCl
2. Size of Anions
Larger the size of anions, greater the covalent character.
Example: LiF, LiCl, LiBr, LiI
LiI is most covalent among the given IA halides as the sixe of iodide ion is larges.
So, the order of covalent character is-
LiI > LiBr > LiCl > LiF

3. Charge on ions (Cations and Anions)
Higher the charge on ions, greater the covalent character.
Example: NaCl, MgCl₂, AlCl₃
AlCl₃ is most covalent among the given molecules as the chage on Al is +3 highest (charge on Na is +1 and on Mg is +2).
So, the order of covalent character is-
AlCl₃ > MgCl₂ > NaCl
4. 18 electron configuration
Molecules which follows 18 electron configuration is more covalent in nature than those molecules which follows 8 electron configuration.
Example: NaCl and CuCl CuCl is more covalent as it follows 18 electron configuration while NaCl is more ionic because it follows 8 electron configuration.

According to Fajan's rules, the covalent nature of ionic compounds is favoured by

a. Large cation and small anion
b. Large cation and large anion
c. Small cation and large anion
d. Small cation and small anion

Maximum covalent character is associated with the compound

a. NaI
b. MgI₂
c. AlCl₃
d. AlI₃

Amongst LiCl, RbCl, BeCl₂ and MgCl₂ the compounds with the greatest and the least ionic character, respectively, are

a. LiCl and RbCl
b. RbCl and BeCl₂
c. RbCl and MgCl₂
d. MgCl₂ and BeCl₂

Molecular Orbital Theory

This theory was put froth by F. Hund and R.S. Mulliken in 1930 and later on developed by I.F. Lennard Jones and Charles Coulson.
The basic posulates of this theory is as follows:
1. When nuclei of two atoms come close to each other, their atomic orbitals interact leading to the formation of molecular orbitals. After the formation of molecular orbitals, atomic orbitals lose their identity.
2. Each molecular orbital is described by a wave function (Ψ) called molecular orbital wave function.
3. The molecular orbital wave function (Ψ) is such that Ψ² represents the probability density or electron charge density.
4. Each molecular orbital wave function is associated with a set of four quantum numbers which determine the energy and the shape of the molecular orbital.
5. Each wave function asssociated with a definite energy value and the total energy of the moleculeis the sum of the energies of the occupied molecular orbitals.
6. Electron fill the molecular orbitals in the same way as they fill the atomic orbitals.
7. Each electron in a molecular orbital belongs to all the nuclei present in the molecules.
8. Each electron moving in a molecular orbital has a spin of +1/2 and -1/2.

Molecular Orbital Diagram

Molecular Orbital

Bonding Molecular Orbital
Bonding molecular orbitals are formed by the combination of atomic orbitals. It has lower energy than that of atomic orbitals from which it is formed.
Electron charge density in between the nuclei is high and hence the repulsion between the nuclei is very low and thus the BMO favours the stable bond formation.
Anti Bonding Molecular Orbital
Antibonding molecular orbitals are formed by the subtraction of atomic orbitals. It has higher energy than that of atomic orbitals from which it is formed.
Electron charge density in between the nuclei is low thus the ABMO does not favours the bond formation.

Hydrogen Bonding

Hydrogen bond is a type of dipole-dipole interaction between very high electronegative atom (i.e.N, O and F) and a hydrogen atom bonded to another electronegative atom. This bond always involves a hydrogen atom. Hydrogen bonds can occur between molecules or within a single molecule.
Hydrogen bond is stronger than van der Waals forces, but weaker than covalent bonds or ionic bonds. It is about 5% the strength of the normal covalent bond formed between O-H.

Types of Hydrogen Bonding

There are two types of Hydrogen bonds. They are-
1. Intermolecular Hydrogen Bonding
2. Intramolecular Hydrogen Bonding

1. Intermolecular Hydrogen Bonding:
When hydrogen bonding takes place between different molecules of the same or different compounds, it is called intermolecular hydrogen bonding. For example – hydrogen bonding in water, alcohol, ammonia, p-nitrophenol etc.


2. Intramolecular Hydrogen Bonding:
The hydrogen bonding which takes place within a molecule itself is called intramolecular hydrogen bonding.
It takes place in compounds containing two groups such that one group contains hydrogen atom linked to an electronegative atom and the other group contains a highly electronegative atom linked to a lesser electronegative atom of the other group. The bond is formed between the hydrogen atoms of one group with the more electronegative atom of the other group.
For example – ortho-nitrophenol, Salicylic acid, Salicyldehyde etc.

Dipole Moment (μ)

Dipole moment is a measure of the polarity of a chemical bond between two atoms in a molecule. Dipole moments occur due to the difference in electronegativity between two chemically bonded atoms. The bond dipole moment is a vector quantity as it has both magnitude and direction.
A dipole moment is the product of the magnitude of the charge and the distance between the centers of the positive and negative charges. It is denoted by the Greek letter 'µ'.
Dipole Moment (µ) = Charge (Q) x distance of separation d)
The unit of Dipole moment is Debye and is denoted by letter 'D'.
1 D = 3.33564 × 10^-30 Coulomb meter.
The dipole moment is used to find the polar nature of the bond. As the magnitude of dipole moment increases, polar nature of the bond in a molecule also increases.
Molecules with zero dipole moment are non-polar in nature, while molecules with net dipole moment are said to be polar in nature.
Dipole moment is also used to find the structure or shape of the molecules. symmetrical structure of the molecule (like CH₄, CCl₄, CO₂, BF₃ etc.) have zero dipole moment. While asymmetrical structure or shape of the molecules (like NH₃, H₂O, CHCl₃ etc.) have net dipole moment. Percentage ionic character in a molecule can be calculated with the help of dipole moment.
Dipole moment can distinguishing between cis- and trans-isomers. Usually, isomer with a higher dipole moment is trans-isomer and isomer with lower dipole moment are cis-isomer.
The dipole moment of para isomer is zero and that of ortho is greater than that of meta.

Dipole Moment and Ionic Character

Polar compounds have covalent as well to ionic character. The ionic character arises due to polarity in the bond. The ionic character can be calculated from the experimentally determined dipole moment.
In H-Cl, the bond distance is 1.26 A^o and dipole moment is 1.03d. If the value of charge be one unit then dipole moment will be-
4.8 x 10⁻¹⁰ x 1.26 x 10⁻⁸ cm = 6.05d.
As the experimental value is 1.03d, the value of charge is less than one i.e. the magnitude of charge is-
1.03/6.05 = 1/6
The percentage ionic character = (experimental dipole moment/Calculated dipole moment) x 100
Thus for HCl-
Percentage ionic character = (1.03d/6.05d) x 100 = 17%
Thus HCl is 17% ionic and 83% covalent.
Ionic character increases as electronegativity difference between the elements increases.